Lesson 3: Changing the Center of Gravity Using Moment Arms Grades 3–4 Objectives Description • To discover that the center of gravity (c.g.) Students discover the center of gravity can be can be changed by adding weights to the changed by adding paper clips to the balanced balanced F-15 ACTIVE model. F-15 ACTIVE cardboard model. • To calculate moment arms using weights on a yardstick. Students calculate the moment arm using a bal- anced yardstick, adding weights at measured Science Standards differences. Unifying Concepts and Processes in Science Materials and Tools Science as Inquiry For each group: Physical Science • Yardstick Positions and Motion of Objects • Rubber band Science and Technology • String Science in Personal and Social • Cellophane tape or masking tape Perspectives • Ruler History and Nature of Science • Weights: -Government Standard weight set Science Process Skills (1, 2, 3 grams) or Observing -Fishing sinkers of known weigh (1, 2, 3 Communicating ounces) or Measuring -Fishing sinkers all one size per group Investigating • Copy of chart for each student Predicting Collecting Data Inferring Hypothesizing

Mathematical Standards String Problem Solving Meterstick Communicating Reasoning Computing and Estimating Measuring Functions

Moment Arm A Moment Arm B Management Rubber Band In part 1, students may work individually or in pairs. In part 2, students working in pairs or groups of three will be able to help each other. Allow 20-30 minutes for part 1 and 45 min- utes for part 2.

Exploring the Extreme: An Educator’s Guide EG-2002-10-001-DFRC 25 Preparation 3. Tell the students to put 3 units of The teacher may want to arrange the hang- weight 4 inches (10.16 cm) from 0 ing yardsticks before class time. Each group point. (3 units weight at 4 inches or will use a suspended yardstick. Wrap a rubber 10.16cm moment arm.) Ask where band around each yardstick. Tie a string to the they could put a 1-unit weight to make rubber band to suspend the yardstick. Move the yardstick balance. Record the the rubber band until the yardstick is balanced. answer. (12 units) Rubber band is at the 0 point and measure- 4. Put 2 units of weight on one side ments will be made in both directions, called to make the yardstick balance. It arms, starting at this point. Explain that mo- will be easier if students use even ment is equal to weight x moment arm (dis- measurements. Record the answer. tance). Calculate moments for tests 1-4. Discussion: Ask if students notice a connection between moments A and B. 1. Tell students to place a 1-unit weight • How do you find moment? 2 inches (5.08 cm) from the 0 point. • What is the difference between They should tape it to the yardstick. moment and moment arm? Suspend the yardstick. It will be unbalanced. Tell students to find out 5. Let students experiment with weights how much weight needs to be placed to get other moments. at 1 inch (2.54 cm) from the 0 point Enrichment: Challenge students to add on the other side to make the yardstick weights to two different spots on the balance. Record the answer on chart. same side. (2 units weight) Weight A1 x Moment arm1 + Weight Discussion: Ask if the larger weight A2 x Moment arm2 = is closer or farther away from 0 point. Weight B x Moment arm B Will this always be true? (Yes, the 1 x 4 + 2 x 3 = 2 x 5 larger weight is always closer to the 0 point.) 2. Tell students to put 2 units of weight at Assessment 6 inches (15.24 cm) from the 0 point. Discussion and Student Sheet Ask them to find what weight needs to be added at 4 inches (10.16 cm) from the 0 point on the other side. Record the answer. (3 units weight) Discussion: The distance the weight is from the 0 point is called the moment arm. One side is called weight A on moment arm A and the other side is weight B on moment arm B. Look at chart.

Exploring the Extreme: An Educator’s Guide EG-2002-10-001-DFRC 26 A B 1. 1 x 2 = 2 1. 2 x 1 = 2 2. 2 x 6 = 12 2. 3 x 4 = 12 3. 3 x 4 = 12 3. 1 x 12 = 12 4. 2 x 3 = 6 4. 3 x 2 = 6 (possible answer) 5. 2 x 6 = 12 5. 3 x 4 = 12 (possible answer) 6. 2 x 9 = 18 6. 3 x 6 = 18 (possible answer)

1 unit 10.16cm 12.7cm 2 units

7.62cm 2 units

Exploring the Extreme: An Educator’s Guide EG-2002-10-001-DFRC 27 Name: ______Date: ______

Moment Student Work Sheet

Distance A Distance B Moment A Moment B Weight A (Moment Weight B (Moment Test # (Grams (Grams (Grams) Arm A, (Grams) Arm B, centimeter) centimeter) Centimeter) centimeter)

#1 28.35g 5.08cm 56.7g 2.54cm

#2 56.7g 15.24cm 85.05g 5.08cm

#3 85.05g 10.16cm 28.35g 30.48cm

#4 56.7g 7.62cm

#5

#6

#7

Exploring the Extreme: An Educator’s Guide EG-2002-10-001-DFRC 28 Name: ______Date: ______

Enrichment Calculate these moments. Use calculators if appropriate.

Exploring the Extreme: An Educator’s Guide EG-2002-10-001-DFRC 29 Exploring the Extreme: An Educator’s Guide EG-2002-10-001-DFRC 30 G r a d e s 5 - 8

Exploring the Extreme: An Educator’s Guide EG-2002-10-001-DFRC 31